Method and apparatus for reducing image artifacts caused by magnet vibration in an MR imaging system

ABSTRACT

A magnetic resonance (MR) imaging system including a method and apparatus for reducing image artifacts caused by magnet vibration is disclosed herein. The system includes a magnetic field vibration quantification and compensation scheme including quantifying a vibration error component included in the magnetic field configured to acquire k-space data corresponding to an MR image, and correcting the k-space data using the vibration error component. The vibration-induced magnetic field perturbation includes a spatially invariant magnetic field, a spatially linear readout magnetic field gradient, a spatially linear phase-encoding magnetic field gradient, and a spatially linear slice-selection magnetic field gradient. The vibration error component can be at least one of a spatially independent phase error of the spatially invariant magnetic field, a k x -space displacement error of the spatially linear readout magnetic field gradient, a k y -space displacement error of the spatially linear phase-encoding magnetic field gradient, and a slice-selection error of the spatially linear slice-selection magnetic field gradient.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. provisional application Ser.No. 60/165,523 by Zhou, entitled “Method and Apparatus for ReducingImage Artifacts caused by Magnet Vibration in a MR Imaging System” filedNov. 15, 1999.

BACKGROUND OF THE INVENTION

The present invention relates generally to magnetic resonance (MR)imaging systems. More particularly, the present invention relates to anMR imaging system equipped to reduce image artifacts caused by magnetvibrations produced therein.

When an object of interest, such as human tissue, is subjected to auniform magnetic field (polarizing field B₀, along the z direction in aCartesian coordinate system denoted as x, y, and z), the individualmagnetic moments of the spins in the tissue attempt to align with thispolarizing field, but precess about it at their characteristic Larmorfrequency. If the object, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, M_(z), may be rotated or“tipped” at a certain tipping angle, into the x-y plane to produce a nettraverse magnetic moment M_(t). A signal is emitted by the excited spinsafter the excitation field B₁ is terminated, and this signal may bereceived and processed to form an MR image.

When utilizing these signals to produce MR images, linear magnetic fieldgradients (G_(x), G_(y), and G_(z)) are also employed. Typically, theobject to be imaged is scanned by a sequence of measurement cycles inwhich these gradient waveforms vary according to the particularlocalization method being used. The resulting set of received nuclearmagnetic resonance (NMR) signals, also referred to as MR signals, aredigitized and processed to reconstruct the image using one of manywell-known reconstruction algorithms.

Ideally, a uniform magnetic field (B₀) and perfectly linear magneticfield gradients (G_(x), G_(y), and G_(z)) would be utilized to image theobject of interest. In reality, however, perturbation to the magneticfield, such as eddy currents, gradient amplifier infidelity, gradientnon-linearity, magnetic field inhomogeneity, and Maxwell terms, canexist, resulting in image artifacts such as blurring, distortion,ghosting, and shift in the reconstructed MR image. In recent years, asmagnets included in MR imaging systems have become smaller in size andweight in order to reduce cost, another perturbation factor is emergingas an important source of image artifacts.

As magnet size and weight are reduced, magnet vibration is becoming anincreasingly serious problem. Magnet vibration causes perturbationmagnetic fields, i.e., magnetic fields with vibration components, to beapplied to the object of interest. In turn, these vibration componentsproduce undesirable image artifacts in the reconstructed MR image.Constrained by cost, it is often difficult to proactively design magnetsto completely eliminate all critical vibration components.

Thus, there is a need for an MR imaging system capable of correcting orcompensating for image artifacts caused by magnet vibration beforereconstructing an MR image. In order to do so, there is a need for an MRimaging system capable of quantifying the magnetic field vibrationcomponents.

BRIEF SUMMARY OF THE INVENTION

One embodiment of the invention relates to a method for reducing imageartifacts caused by magnet vibration in an MR imaging system. The methodincludes quantifying a vibration error component included in aperturbation magnetic field. The perturbation magnetic field iscompensated to acquire k-space data corresponding to an MR image.

Another embodiment of the invention relates to an MR imaging system forreducing image artifacts caused by magnet vibration. The system includesa system control. The system control is capable of configuring acompensating magnetic field to offset a perturbation magnetic fieldproduced by magnet vibration. The system control is further capable ofcalculating a vibration error component included in the perturbationmagnetic field.

Still another embodiment of the invention relates to an MR imagingsystem for reducing image artifacts caused by magnet vibration. Thesystem includes means for configuring a pulse sequence to acquirek-space data corresponding to an MR image. The pulse sequence includescompensating magnetic fields. The system further includes means forcalculating a vibration error component included in the pulse sequence.The means for configuring is coupled to the means for calculating.

BRIEF DESCRIPTION OF THE DRAWINGS

The preferred embodiment will become more fully understood from thefollowing detailed description, taken in conjunction with theaccompanying drawings, wherein like reference numerals denote likeelements, in which:

FIG. 1 is a block diagram of a magnetic resonance (MR) imaging systemwhich employs an embodiment of the present invention;

FIG. 2 is an electrical block diagram of a transceiver block which formspart of the MR imaging system of FIG. 1;

FIG. 3 is a flowchart of a magnetic field vibration quantification andcompensation scheme implemented in the MR imaging system of FIG. 1;

FIG. 4 is a simplified diagram of a spin echo (SE) pulse sequence usedin one embodiment of the scheme of FIG. 3;

FIG. 5 is a waveform diagram including a part of the correctiontechnique of the scheme of FIG. 3;

FIG. 6 is a simplified diagram of a fast gradient echo (FGRE) pulsesequence used in another embodiment of the scheme of FIG. 3;

FIG. 7 is a simplified diagram of a fast spin echo (FSE) pulse sequenceused in still another embodiment of the scheme of FIG. 3; and

FIG. 8 is a waveform diagram including a part of the correctiontechnique of the scheme of FIG. 3.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, there is shown the major components of a magneticresonance (MR) imaging system. The operation of the system is controlledfrom an operator console 100 which includes an input device 101, acontrol panel 102, and a display 104. The console 100 communicatesthrough a link 116 with a separate computer system 107 that enables anoperator to control the production and display of images on the screen104. The computer system 107 includes a number of modules whichcommunicate with each other through a backplane. These include an imageprocessor module 106, a CPU module 108 and a memory module 113, known inthe art as a frame buffer for storing image data arrays. The computersystem 107 is linked to a disk storage 111 and a tape drive 112 forstorage of image data and programs, and it communicates with a separatesystem control 122 through a high speed serial link 115.

The system control 122 includes a set of modules connected together by abackplane. These include a CPU module 119 and a pulse generator module121 which connects to the operator console 100 through a serial link125. It is through this link 125 that the system control 122 receivescommands from the operator which indicate the scan sequence that is tobe performed. The pulse generator module 121 operates the systemcomponents to carry out the desired scan sequence. It produces datawhich indicate the timing, strength and shape of RF pulses, and thetiming of and length of a data acquisition window. The pulse generatormodule 121 connects to a set of gradient amplifiers 127, to control thetiming and shape of the gradient pulses to be produced during the scan.The pulse generator module 121 also receives patient data from aphysiological acquisition controller 129 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes or respiratory signals from a bellows. Andfinally, the pulse generator module 121 connects to a scan roominterface circuit 133 which receives signals from various sensorsassociated with the condition of the patient and the magnet system. Itis also through the scan room interface circuit 133 that a patientpositioning system 134 receives commands to move the patient to thedesired position for the scan.

The gradient waveforms produced by the pulse generator module 121 areapplied to a gradient amplifier system 127 comprised of G_(x), G_(y),and G_(z) amplifiers. Each gradient amplifier excites a correspondinggradient coil in an assembly generally designated 139 to produce themagnetic field gradients used for spatially encoding acquired signals.The gradient coil assembly 139 forms part of a magnet assembly 141 whichincludes a polarizing magnet 140 and a whole-body RF coil 152.

A transceiver module 150 in the system control 122 produces pulses whichare amplified by an RF amplifier 151 and coupled to the RF coil 152 by atransmit/receiver switch 154. The resulting signals emitted by theexcited nuclei in the patient may be sensed by the same RF coil 152 andcoupled through the transmit/receive switch 154 to a preamplifier 153.The amplified MR signals are demodulated, filtered, and digitized in thereceiver section of the transceiver 150. The transmit/receive switch 154is controlled by a signal from the pulse generator module 121 toelectrically connect the RF amplifier 151 to the coil 152 during thetransmit mode and to connect the preamplifier 153 during the receivemode. The transmit/receive switch 154 also enables a separate RF coil(for example, a head coil or surface coil) to be used in either thetransmit or receive mode.

The MR signals picked up by the RF coil 152 are digitized by thetransceiver module 150 and transferred to a memory module 160 in thesystem control 122. When the scan is completed and an entire array ofdata has been acquired in the memory module 160, an array processor 161operates to Fourier transform the data into an array of image data. Theimage data are conveyed through the serial link 115 to the computersystem 107 where they are stored in the disk memory 111. In response tocommands received from the operator console 100, these image data may bearchived on the tape drive 112, or they may be further processed by theimage processor 106 and conveyed to the operator console 100 andpresented on the display 104.

Referring particularly to FIGS. 1 and 2, the transceiver 150 producesthe RF excitation field B₁ through power amplifier 151 at a coil 152Aand receives the resulting signal induced in a coil 152B. As indicatedabove, the coils 152A and B may be separate as shown in FIG. 2, or theymay be a single wholebody coil as shown in FIG. 1. The base, or carrier,frequency of the RF excitation field is produced under control of afrequency synthesizer 200 which receives a set of digital signals fromthe CPU module 119 and pulse generator module 121. These digital signalsindicate the frequency and phase of the RF carrier signal produced at anoutput 201. The commanded RF carrier is applied to a modulator and upconverter 202 where its amplitude is modulated in response to a signalR(t) also received from the pulse generator module 121. The signal R(t)defines the envelope of the RF excitation pulse to be produced and isproduced in the module 121 by sequentially reading out a series ofstored digital values. These stored digital values may, in turn, bechanged from the operator console 100 to enable any desired RF pulseenvelope to be produced.

The magnitude of the RF excitation pulse produced at output 205 isattenuated by an exciter attenuator circuit 206 which receives a digitalcommand from the backplane 118. The attenuated RF excitation pulses areapplied to the power amplifier 151 that drives the RF coil 152A. For amore detailed description of this portion of the transceiver 122,reference is made to U.S. Pat. No. 4,952,877 which is incorporatedherein by reference.

Referring still to FIGS. 1 and 2, the MR signal produced by the subjectis picked up by the receiver coil 152B and applied through thepreamplifier 153 to the input of a receiver attenuator 207. The receiverattenuator 207 further amplifies the signal by an amount determined by adigital attenuation signal received from the backplane 118.

The received signal is at or around the Larmor frequency, and this highfrequency signal is down converted in a two step process by a downconverter 208 which first mixes the MR signal with the carrier signal online 201 and then mixes the resulting difference signal with the 2.5 MHzreference signal on line 204. The down converted MR signal is applied tothe input of an analog-to-digital (A/D) converter 209 which samples anddigitizes the analog signal and applies it to a digital detector andsignal processor 210 which produces 16 bit in-phase (I) values and16-bit quadrature (Q) values corresponding to the received signal. Theresulting stream of digitized I and Q values of the received signal areoutput through backplane 118 to the memory module 160 where they arenormalized in accordance with the present invention and then employed toreconstruct an image.

Mechanical vibration produced by magnet assembly 141 in the course of anMR image acquisition causes a non-ideal magnetic field to perturb animage data set corresponding to an object of interest. This non-idealmagnetic field, or a vibrating magnetic field b(t), causes the imagedata set to be non-ideal such that the reconstructed MR image can havevarious image quality problems such as distortion, ghosting, imageshift, shading, blurring, and intensity variation. Hence, by identifyingand quantifying one or more magnetic field vibration error componentsand compensating for these error components, image artifacts which wouldotherwise appear in the reconstructed MR image can be minimized oreliminated.

Vibrating magnetic field b(t), irrespective of its vibrational modes,must satisfy the Laplace equation ∇² b(t)=0. Thus, vibrating magneticfield b(t) can be described by the summation of its various spatialcomponents (or spherical harmonics):

b(t)=b _(o)(t)+g _(x)(t)x+g _(y)(t)y+g _(z)(t)z+. . .   (1)

where b_(o)(t) is a spatially invariant magnetic field; g_(x)(t),g_(y)(t), and g_(z)(t) are spatially linear gradient magnetic fields inthe x, y, and z directions, respectively; and the omitted terms arespatially higher order magnetic fields. Notice that all the terms inEquation (1) depend on a time variable t. Typically, b_(o)(t) is alsoreferred to as a main magnetic field perturbation, g_(x)(t) as afrequency-encoding or readout gradient perturbation, g_(y)(t) as aphase-encoding gradient perturbation, and g_(z)(t) as a slice-selectiongradient perturbation.

It shall be assumed that the higher order gradient terms containnegligible vibration error components so that vibrating magnetic fieldb(t) can be approximated by the four terms explicitly shown in Equation(1). It should be understood, however, that a quantification andcompensation scheme, to be described in greater detail hereinafter, maybe implemented for the vibrating magnetic field b(t) including spatiallyhigher order magnetic field terms.

Each of the four terms in Equation (1) may include multiple vibrationalcomponents, each component being defined by four parameters—anamplitude, a frequency, a phase, and a damping time constant.Accordingly, b_(o)(t) can be expressed as: $\begin{matrix}{{b_{0}(t)} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}^{{- t}/\lambda_{m}}{\sin \left( {{2\quad \pi \quad f_{m}t} + \zeta_{m}} \right)}}}} & \text{(2a)}\end{matrix}$

where M_(o) is the total number of vibrational modes, a_(m) is anamplitude, f_(m), is a frequency, ζ_(m) is a phase, λ_(m) is a dampingtime constant, and m is an index of the vibrational mode. Similarly, thethree linear gradient terms (g_(x)(t), g_(y)(t), and g_(z)(t)) inEquation (1) can be expressed as: $\begin{matrix}{{g_{x}(t)} = {\sum\limits_{m = 1}^{M_{x}}{g_{x,m}^{{- t}/\lambda_{x,m}}{\sin \left( {{2\quad \pi \quad f_{x,m}t} + \zeta_{x,m}} \right)}}}} & \text{(2b)} \\{{g_{y}(t)} = {\sum\limits_{m = 1}^{M_{y}}{g_{y,m}^{{- t}/\lambda_{y,m}}{\sin \left( {{2\quad \pi \quad f_{y,m}t} + \zeta_{y,m}} \right)}}}} & \text{(2c)} \\{{g_{z}(t)} = {\sum\limits_{m = 1}^{M_{z}}{g_{z,m}^{{- t}/\lambda_{z,m}}{\sin \left( {{2\quad \pi \quad f_{z,m}t} + \zeta_{z,m}} \right)}}}} & \text{(2d)}\end{matrix}$

where M_(x), M_(y), and M_(z) are the total number of vibrational modes;g_(x,m), g_(y,m), and g_(z,m) are the amplitudes; f_(x,m), f_(y,m), andf_(z,m) are the frequencies; ζ_(x,m), ζ_(y,m), and ζ_(z,m) are thephases; and λ_(x,m), λ_(y,m), and λ_(z,m) are the damping time constantsfor g_(x)(t), g_(y)(t), and g_(z)(t), respectively.

If we assume that the damping effect is negligible during dataacquisition, Equations (2a)-(2d) can be simplified to: $\begin{matrix}{{b_{0}(t)} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}\sin \quad \left( {{2\quad \pi \quad f_{m}t} + \zeta_{m}} \right)}}} & \text{(3a)} \\{{g_{x}(t)} = {\sum\limits_{m = 1}^{M_{x}}{g_{x,m}\sin \quad \left( {{2\quad \pi \quad f_{x,m}t} + \zeta_{x,m}} \right)}}} & \text{(3b)} \\{{g_{y}(t)} = {\sum\limits_{m = 1}^{M_{y}}{g_{y,m}\sin \quad \left( {{2\quad \pi \quad f_{y,m}t} + \zeta_{y,m}} \right)}}} & \text{(3c)} \\{{g_{z}(t)} = {\sum\limits_{m = 1}^{M_{z}}{g_{z,m}\sin \quad \left( {{2\quad \pi \quad f_{z,m}t} + \zeta_{z,m}} \right)}}} & \text{(3d)}\end{matrix}$

The above simplification is being introduced to ease the description ofthe present invention. It should be understood that the presentinvention may be implemented using Equations (2a)-(2d), i.e., withnon-negligible damping effect, instead of Equations (3a)-(3d).

To image the object of interest or a portion thereof, one or more pulsesequences (i.e., RF pulses and gradient pulses) is configured to induceand acquire a p×q array of raw k-space data points, comprising p columnsof k_(x)-space data and q rows of k_(y)-space data. The pulse sequencecauses one or more MR signals to be emitted from the excited object ofinterest and acquires the MR signal. Each MR signal provides one row ofk_(y)-space data having p data points. In this manner, sampling a totalof q MR signals will result in acquiring the p×q array of raw k-spacedata points, sufficient to perform image reconstruction of the object ofinterest.

Referring to FIG. 3, there is shown a flowchart of the magnetic fieldvibration quantification and compensation scheme. The scheme includes astart loop step 600, a prepare magnetic field b(t) step 602, a calculatevibration component of b_(o,n)(t) step 604, a calculate vibrationcomponent of g_(x,n)(t) step 606, a calculate vibration component ofg_(y,n)(t) step 608, a calculate vibration component of g_(z)(t) step610, an initiate image data acquisition step 612, a compensate errorinduced by g_(z)(t) vibration component step 614, a compensate errorinduced by b_(o,n)(t) vibration component step 616, a compensate errorinduced by g_(x,n)(t) vibration component step 618, a compensate errorinduced by g_(y,n)(t) vibration component step 620, an imagereconstruction step 622, a decision step 624, an end loop step 626, andan incrementor step 628. This scheme is performed n=1, 2, . . . , qtimes such that all vibration error components corresponding to thevibrating magnetic field b(t) for each MR echo signal, or in anotherwords, each row of k-space data, can be identified, quantified, andutilized to perform the error compensation on the corresponding k-spacedata. The vibration error components calculated in steps 604-610 areutilized by the system control 122 and/or the computer system 107 toperform the compensate steps 614-620. Since the actual equationsinvolved in the quantification and compensation scheme will varyslightly depending on the type of pulse sequence implemented to acquirethe MR image, the scheme will be illustrated using three different pulsesequences: a spin-echo (SE) pulse sequence, a fast gradient echo (FGRE)pulse sequence, and a fast spin echo (FSE) pulse sequence.

SE Pulse Sequence

In one embodiment of the present invention, an operator initiates the MRimaging system, i.e., start loop step 600, to acquire the MR image ofthe object of interest using the SE pulse sequence. Depending on thecapabilities of the MR imaging system, the operator may directly specifythe SE pulse sequence from among a list of pulse sequences; the systemmay be preset to the SE pulse sequence; or based on scan time, imageresolution, type of tissue to be imaged, and other requirements, thesystem may select the SE pulse sequence. Once the SE pulse sequence hasbeen chosen, this pulse sequence will be configured including carryingout the prepare vibrating magnetic field b(t) step 602. Prepare step 602includes configuring the frequencies, amplitudes, and initial phases ofb_(o)(t), g_(x)(t), g_(y)(t), and g_(z)(t) comprising b(t).

Referring to FIG. 4, there is shown a simplified waveform diagram of theSE pulse sequence. As is well-known in the art, the SE pulse sequenceincludes a 90° RF pulse 300, a 180° RF pulse 302, and a data acquisitionwindow 304 (during which the readout gradient is on). A reference timepoint of t=0 is set at the center of the 90° RF pulse 300 of a firstrepetition cycle (or TR). The time from the 90° RF pulse 300 to the 180°RF pulse 302 is referred to as a half echo time τ. The data acquisitionwindow 304 is turned on after the 180° RF pulse 302, from t₁≦t≦t₁+T,where time t₁<2τ and T is a duration of the data acquisition window. Thedata acquisition window 304 is also referred to as an analog-to-digitalconverter (ADC) window.

Shown in FIG. 4, the data acquisition window 304 indicates a fractionalecho center 306, located at a time t=t₁+d, and a full echo center 308,located as a time t=t₁+d+Δ. The scheme is applicable for the SE pulsesequence including a fractional echo acquisition or a full echoacquisition. The full echo acquisition case can be considered as aspecial case of the fractional echo acquisition in which Δ=0. From FIG.4, a fractional echo parameter can be defined as: $\begin{matrix}{{{frac\_ echo} = {1 - \frac{2\Delta}{T}}},} & \text{(4a)}\end{matrix}$

and the following timing relationship can be derived: $\begin{matrix}{{t_{1} = {{2\tau} - {\frac{T}{2}({frac\_ echo})}}},{and}} & \text{(4b)} \\{T = \frac{k_{xres}}{2 \cdot {rbw}}} & \text{(4c)}\end{matrix}$

where rbw is a receiver bandwidth (i.e., the signal frequency rangesfrom −rbw to +rbw) and k_(xres) is the total number of acquired k-spacedata points along the readout direction (i.e., k_(xres)=p). The SE pulsesequence will be configured to have a time period TR and to repeat atotal of q times (with slight changes to the nominal phase-encodinggradient G_(y) in each nth TR, where n=1, 2, . . . , q) to acquire all qrows of k-space data.

Once the SE pulse sequence has been configured, the calculate vibrationcomponent steps 604-610 will be carried out. Preferably, steps 604-610for the nth echo or TR are completed before the corresponding pulsesequence for the nth echo or TR is applied to the object of interest toacquire the nth row of k-space data. Although steps 604-610 are shown insuccessive order, steps 604-610 may be performed in any order or evensimultaneously as long as steps 604-610 are completed prior to theinitiation of the nth pulse sequence. In this manner, the vibrationerror components can be compensated for before, during, or after thedata acquisition.

Turning to the calculate vibration component of b_(o,n)(t) step 604, thevibration error component for b_(o)(t) produces a phase error φ_(o)(t).For each TR time period, the phase error φ_(o)(t) can be expressed bythree terms: (1) the first term covering the time period from the 90° RFpulse 300 to the 180° RF pulse 302 (0≦t≦τ); (2) the second term coveringthe time period from the 180° RF pulse 302 to the beginning of the dataacquisition window 306 (τ≦t≦t₁); and (3) the third term covering thetime period during the data acquisition window 306 (t₁≦t′≦t) (see FIG.4).

Thus, phase error φ_(o)(t) for the first TR (i.e., n=1) is:$\begin{matrix}{{\varphi_{0}(t)} = {{{- 2}\quad \pi \quad \gamma {\int_{0}^{\tau}{{b_{0}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t_{1}}{{b_{0}(t)}{t}}}} + {2\quad {\pi\gamma}{\int_{t_{1}}^{t}{{b_{0}\left( t^{\prime} \right)}{t^{\prime}}}}}}} & (5)\end{matrix}$

where γ is a gyromagnetic constant, the first term includes a negativesign to take into account the phase reversal effect of the 180° RFpulse, and b_(o)(t) is provided in Equation (3a). The phase errorφ_(o)(t) represents the total phase error (or vibration error component)from the vibrating b_(o)(t) that will occur for the first TR periodduring the data acquisition.

Since the SE pulse sequence will repeat after the first TR, the phaseerrors for all the subsequent TR periods can be calculated usingEquation (5) modified by a new b_(o)(t) appropriate for each particularTR interval. It can be seen that for any time t′ within the first TRperiod (at t=t′), b_(o)(t) in the first TR period is: $\begin{matrix}{{b_{0,1}\left( t^{\prime} \right)} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}{\sin \left( {{2\quad \pi \quad f_{m}t^{\prime}} + \zeta_{m}} \right)}}}} & \text{(6a)}\end{matrix}$

and b_(o)(t) at any time within the second TR period (at t=t′+TR) is:$\begin{matrix}\begin{matrix}{b_{0,2} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}{\sin\left( {{2\quad \pi \quad {f_{m}\left( {t^{\prime} + {TR}} \right)}} + \zeta_{m}} \right\rbrack}}}} \\{= {\sum\limits_{m = 1}^{M_{0}}{a_{m}{\sin\left( {{2\quad \pi \quad f_{m}t^{\prime}} + {2\quad \pi \quad f_{m}{TR}} + \zeta_{m}} \right\rbrack}}}} \\{= {\sum\limits_{m = 1}^{M_{0}}{a_{m}{\sin \left\lbrack {{2\quad \pi \quad f_{m}t^{\prime}} + \zeta_{m,1}} \right\rbrack}}}}\end{matrix} & \text{(6b)}\end{matrix}$

where the time variable t in b_(o)(t) of Equation (3a) has beensubstituted with t′ and t′+TR in Equations (6a) and (6b), respectively.With this substitution, it is apparent that b_(o)(t) at the second TR(i.e., b_(o,2)(t)) is essentially the same as b_(o)(t) at the first TR(i.e., b_(o,1)(t)) except that the phase ζ_(m) in Equation (6a) has beenchanged to:

ζ_(m,1)=2πf _(m) TR+ζ _(m).  (6c)

Accordingly, b_(o)(t) in Equation (3a) at any TR period for a given MRimage acquisition can be more generally expressed as: $\begin{matrix}{{b_{0,n}(t)} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}{\sin \left( {{2\quad \pi \quad f_{m}t} + \xi_{m,{n - 1}}} \right)}}}} & \text{(7a)}\end{matrix}$

where n=1, 2, . . . , q; q=total number of TR periods or rows of k-spacedata; 0≦t ≦TR for the nth TR; and ζ_(m,n−1)=2π(n−1)f_(m)TR +ζ_(m).

Then Equation (5) can be generalized to calculate a phase errorφ_(o,n)(t) of b_(o,n)(t) for any nth TR period within a given MR imageacquisition: $\begin{matrix}\begin{matrix}{{\varphi_{0,n}(t)} = \quad {{{- 2}\quad \pi \quad \gamma {\int_{0}^{\tau}{{b_{0,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t_{1}}{{b_{0,n}(t)}{t}}}} +}} \\{\quad {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{b_{0,n}\left( t^{\prime} \right)}{{t^{\prime}}.}}}}}\end{matrix} & \text{(7b)}\end{matrix}$

Hence in step 604, the phase error φ_(o,n)(t) of b_(o,n)(t) for the nthrow of k-space data to be acquired is calculated using Equations (7a)and (7b). Depending on the form of b_(o,n)(t), φ_(o,n)(t) for the nthecho or TR can be solved either numerically or analytically.

For the calculate vibration component of g_(x,n)(t) step 606, thevibration error component of g_(x)(t) produces a k_(x)-spacedisplacement error Δk_(x)(t). The k_(x)-space displacement errorΔk_(x)(t) results in k-space data distortion in the k_(x) direction.

Similar to the characterization or derivation of b_(o)(t) to b_(o,n)(t)in Equation (7a), g_(x)(t) in Equation (3b) can be characterized withrespect to the nth TR period to: $\begin{matrix}{{g_{x,n}(t)} = {\sum\limits_{m = 1}^{M_{x}}{g_{x,m}{\sin \left( {{2\quad \pi \quad f_{x,m}t} + \zeta_{x,m,{n - 1}}} \right)}}}} & \text{(8a)}\end{matrix}$

where ζ_(x,m,n−1)=2π(n−1)f_(x,m)TR+ζ_(x,m). Then Δk_(x,n)(t) for the nthTR can be calculated using Equation (7b) with the substitution ofb_(o,n)(t) with g_(x,n)(t) in Equation (8a): $\begin{matrix}\begin{matrix}{{\Delta \quad {k_{x,n}(t)}} = \quad {{{- 2}\quad \pi \quad \gamma {\int_{0}^{\tau}{{g_{x,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t_{1}}{{g_{x,n}(t)}{t}}}} +}} \\{\quad {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{g_{x,n}\left( t^{\prime} \right)}{{t^{\prime}}.}}}}}\end{matrix} & \text{(8b)}\end{matrix}$

Hence in step 606, the k_(x)-space displacement error Δk_(x,n)(t) ofg_(x,n)(t) for the nth row of k-space data to be acquired is calculatedusing Equations (8a) and (8b). Depending on the form of g_(x,n)(t),Δk_(x,n)(t) can be solved either numerically or analytically.

For the calculate vibration component of g_(y,n)(t) step 608, thevibration error component of g_(y)(t) produces a k_(y)-spacedisplacement error Δk_(y)(t). The k_(y)-space displacement error causesk-space data points to be distorted in the k_(y) direction. Thephase-encoding gradient error of g_(y)(t) is the counterpart to thereadout gradient error of g_(x)(t), and Equations (8a) and (8b) needmerely be modified to yield g_(y,n)(t) and Δk_(y,n)(t): $\begin{matrix}{{g_{y,n}(t)} = {\sum\limits_{m = 1}^{M_{y}}{g_{y,m}{\sin \left( {{2\quad \pi \quad f_{y,m}t} + \zeta_{y,m,{n - 1}}} \right)}}}} & \text{(9a)} \\\begin{matrix}{{\Delta \quad {k_{y,n}(t)}} = \quad {{{- 2}\quad \pi \quad \gamma {\int_{0}^{\tau}{{g_{y,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t_{1}}{{g_{y,n}(t)}{t}}}} +}} \\{\quad {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{g_{y,n}\left( t^{\prime} \right)}{t^{\prime}}}}}}\end{matrix} & \text{(9b)}\end{matrix}$

where g_(y,n)(t) is g_(y)(t) in Equation (3c) expressed with respect tothe nth TR period and ζ_(y,m,n−1)=2π(n−1)f_(y,m)TM+ζ_(y,m). Hence instep 608, the k_(y)-space displacement error Δk_(y,n)(t) of g_(y,n)(t)for the nth row of k-space data to be acquired is calculated usingEquations (9a) and (9b). The k_(y)-space displacement error Δk_(y,n)(t)may be mathematically solved by numerical or analytical methods.

For the calculate vibration component of g_(z)(t) step 610, thevibration error component of g,(t) produces a slice-selection gradienterror Δk_(z). Unlike φ_(0,n)(t), Δk_(x,n)(t), and Δk_(y,n)(t), Δk_(z)can be approximated with a time-independent function, Δk_(z,n) which isevaluated using a time interval from the nth 90° RF pulse to the centerof the nth echo. Taking into account the phase reversal effect of thenth 180° RF pulse, Δk_(z,n) for the nth TR is: $\begin{matrix}{{\Delta \quad k_{z,n}} = {2\quad \pi \quad {\gamma \left\lbrack {{- {\int_{{({n - 1})}{TR}}^{{{({n - 1})}{TR}} + \tau}{{g_{z}(t)}{t}}}} + {\int_{{{({n - 1})}{TR}} + \tau}^{{{({n - 1})}{TR}} + {2\tau}}{{g_{z}(t)}{t}}}} \right\rbrack}}} & (10)\end{matrix}$

where g_(z)(t) is given by Equation (3d). Similar to Equations (7b),(8b), and (9b), Equation (10) can also be expressed as: $\begin{matrix}{{{\Delta \quad {k_{z,n}(t)}} = {{{- 2}\quad \pi \quad \gamma {\int_{0}^{\tau}{{g_{z,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{2\quad \tau}{{g_{z,n}(t)}{t}}}}}},} & \text{(10a)}\end{matrix}$

 where $\begin{matrix}{{{g_{z,n}(t)} = {\sum\limits_{m = 1}^{M_{z}}{g_{z,n}{\sin \left( {{2\quad \pi \quad f_{z,m}t} + \zeta_{z,m,{n - 1}}} \right)}}}},} & \text{(10b)}\end{matrix}$

 ζ_(z,m,n−1)=2π(n−1)f _(z,m) TR+ζ _(z,m).   (10c)

After steps 604-610 have been carried out, the next step is the initiateimage data acquisition step 612. In step 612, the SE pulse sequenceconfigured to acquire the nth row of k-space data is applied to theobject of interest.

The compensate step 614 occurs prior to the image data acquisition ofthe nth row of k-space data. Preferably, the slice-selection gradientG_(z)(t) for the nth TR is modified by including a correction pulse orwaveform configured from the calculated Δk_(z,n) for the nth TR. Asshown in FIG. 5, the correction pulse or waveform can be (a) a blipgradient pulse 310 g_(zcomp1) (see FIG. 5(a)) having an area under thepulse of −Δk_(z,n)/2πγ, or (b) an additional crusher or slice refocusinggradient pulse 312 g_(comp2) (see FIG. 5(b)) also having an area underthe pulse of −Δk_(z,n)/2πγ. In either case, the correction pulse orwaveform functions to “cancel” the Δk_(z,n) error induced by theoriginal vibrating g_(z)(t) for the nth TR.

Although the blip gradient pulse 310 is shown in FIG. 5(a) as occurringafter the nth 180° RF pulse, it can alternatively perform thecompensation from any time after the nth 90° RF pulse to before thestart of the nth echo. The shape of the blip gradient pulse 310 isflexible, and not limited to the triangular shape shown. However, if apositive pulse is used in the time period between the 180° RF pulse andthe start of the echo, then a negative pulse would have to beimplemented when used in the time period between the 90° and 180° RFpulses (to offset the phase reversal effect of the 180° RF pulse).Similarly, the additional gradient pulse 312 can also occur at any timeafter the 90° RF pulse to before the start of the echo, be any pulseshape, and would have to flip the polarity when between the 90° and 180°RF pulses.

In FIG. 3, although steps 614-620 are shown in consecutive order, steps614-620 do not necessarily follow this order and may be performedsimultaneously. In the compensate step 616, the phase error φ_(o,n)(t)induced by b_(o,n)(t) can be compensated for in the nth row of k-spacedata after the data acquisition but before image reconstruction. Thecompensation or correction comprises using the phase error φ_(o,n)(t)for the nth TR (calculated using Equation (7b)) to perform a phasesubtraction with each k-space data point in the nth row. In this manner,image artifacts which will result from the perturbing (i.e., vibrating)b_(o,n)(t) is minimized or eliminated. For a more detailed descriptionof the phase subtraction correction method, reference is made to U.S.Pat. No. 5,642,047 owned by the General Electric Company, which isincorporated herein by reference.

Alternatively, instead of correcting k-space data that are vibrationcontaminated (i.e., correction after data acquisition), compensate step616 may comprise performing the correction of φ_(o,n)(t) for the nth TRwhile the nth row data acquisition is in progress. The phase errorφ_(o,n)(t) for the nth TR can be compensated for by dynamicallyadjusting the phase of the receiver portion of transceiver 150. Usingthis approach, although the MR echo signal emitted from the object ofinterest is vibration contaminated, the data acquired are free of thevibration error because the data acquisition or receiving apparatusitself is being used to offset the error and acquire the correct data.In still another alternative, phase error φ_(o,n)(t) for the nth TR maybe corrected for by accordingly adjusting the main magnetic field orchanging the receiver frequency for the nth TR before the acquisition ofthe nth k-space data. This pre-execution compensation approach isparticularly effective when b_(o,n)(t) is a constant value for theentire nth row of k-space. For a more detailed description of thecorrection methods employing adjustment of the receiver phase andfrequency, references are made to U.S. Pat. Nos. 5,864,233 and5,923,168, both owned by the General Electric Company, which areincorporated herein by reference.

In the compensate steps 618, 620, the k_(x)-space displacement errorΔk_(x,n)(t) induced by g_(x,n)(t) and the k_(y)-space displacement errorΔk_(y,n)(t) induced by g_(y,n)(t), respectively, will be compensated forin the nth row of acquired k-space data before image reconstruction. Thedisplacement errors Δk_(x,n)(t) and Δk_(y,n)(t) for the nth TR(calculated using Equations (8b) and (9b)) are used to restore thedistorted k-space to a rectilinear grid using one of known regriddingalgorithms. For more details relating to regridding algorithms,reference is made to “Selection of a Convolution Function for FourierInversion Using Gridding” by J. I. Jackson et al., IEEE Transactions inMedical Imaging, 10: 473-478 (1991), which is incorporated herein byreference.

Alternatively, the gradient errors caused by the magnet vibration,g_(x,n)(t) and g_(y,n)(t), for the nth TR can be compensated throughpulse sequence modification. In this approach, each of the two errorterms of g_(x,n)(t) and g_(y,n)(t), respectively, is further dividedinto a pre-acquisition error and an acquisition error.

The pre-acquisition errors associated with g_(x,n)(t) and g_(y,n)(t) aredescribed by two k-space offsets for the nth row of k-space data, shownin Equations (11a) and (11b), respectively: $\begin{matrix}{{{\Delta \quad k_{x,n,{pre}}} = {{{- 2}\quad \pi \quad \gamma {\int_{o}^{\tau}{{g_{x,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t1}{{g_{x,n}(t)}{t}}}}}},{and}} & \text{(11a)} \\{{\Delta \quad k_{y,n,{pre}}} = {{{- 2}\quad \pi \quad \gamma {\int_{o}^{\tau}{{g_{y,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{\tau}^{t1}{{g_{y,n}(t)}{{t}.}}}}}} & \text{(11b)}\end{matrix}$

The pre-acquisition errors can be compensated using a readout and aphase-encoding gradient pulse whose area equals to −Δk_(x,npre)/(2πγ)and −Δk_(y,n,pre)/(2πγ), respectively. The compensatory gradient pulsesmay be independent pulses or may be combined with the existing gradientpulses, such as the dephasing readout gradient pulse and the nominalphase-encoding gradient pulses.

The acquisition errors are described as two perturbation gradients onthe readout and phase-encoding gradient axes, respectively:

g_(x,n,acq)(t)=g_(x,n)(t) with t ₁ ≦t<t ₁ +T,  (11c)

g_(y,n,acq)(t)=g_(y,n)(t) with t ₁ ≦t<t ₁ +T.  (11d)

The readout gradient error g_(x,n,acq)(t) can be compensated by changingthe nominal readout gradient from G_(x)(t) to G_(x)(t)−g_(x,n,acq)(t).The phase-encoding gradient error gy,n acq(t) can be compensated byadding a cancellation gradient equal to −g_(y,n,acq)(t) to thephase-encoding gradient axis concurrent with the readout gradient.Unlike the previous k-space correction method using regridding, thecompensation approach based on pulse sequence modification producesk-space data free from the vibration effects. Therefore, the acquiredk-space data can be directly used for image reconstruction.

In decision step 624, if all the rows of k-space data for a given MRimage have not been corrected (i.e., n<q), then decision step 624directs the calculations and corrections relating to the next vibrationerror components (i.e., n=n+1 in step 628) to be performed. Otherwise,if all the rows of k-space data for a given MR image have been corrected(i.e., n=q), then decision step 624 directs the magnetic field vibrationquantification and compensation process to end for this MR image. Next,image reconstruction is carried out in step 622. Image reconstruction ispossible using any one of well-known reconstruction techniques such as aFourier transform with Fermi filters or a Homodyne reconstructionalgorithm for fractional echo or fractional number of excitations (NEX)data sets. The reconstructed image data set, which should now includeminimal or no image artifacts caused by magnet vibration, is suitablefor image display, storage, transmission to a remote site, film or printrecord, or other utilization and manipulations, for use in, for example,medical diagnosis or further processing.

FGRE Pulse Sequence

In another embodiment of the present invention, the magnetic fieldvibration quantification and compensation scheme is applied to an MRimage acquired using the FGRE pulse sequence. Much of the abovedescription of the scheme with respect to the SE pulse sequence is alsoapplicable with respect to the FGRE pulse sequence. Equations, timeintervals of interest, and/or other parameters unique to theimplementation of the FGRE pulse sequence will be discussed below.

Once the FGRE pulse sequence has been chosen, the start loop step 600 isentered to initiate the quantification and compensation scheme. Next,the prepare b(t) step 602 is carried out as part of the configuration ofthe FGRE pulse sequence. Prepare step 602 includes configuring orspecifying the frequencies, amplitudes, and initial phases of b_(o)(t),g_(z)(t), g_(y)(t), and g_(z)(t) comprising b(t).

Referring to FIG. 6, there is shown a simplified diagram of the FGREpulse sequence. As is well-known in the art, the FGRE pulse sequenceincludes an (α° RF pulse 400 and a data acquisition window 402 (duringwhich the readout gradient G_(x)(t) is active). The α° RF pulse 400 isan RF pulse with α typically ranging from 5 to 90 degrees, andpreferably between 30 to 60 degrees. A reference time point of t=0 isset at the center of the α° RF pulse 400 of the first TR. The dataacquisition window 402, also referred to as an analog-to-digitalconverter (ADC) window, is turned on at time t=t₁ after the α° RF pulse400 and remains on for a T time period. A fractional echo center 404,located at a time t=t₁+d, and a full echo center 406, located at a timet=t₁+d+Δ, are also shown with respect to window 402, where Δ is theseparation between the peak of the MR echo signal and the center of thewindow 402. The FGRE pulse sequence is intended to cover both afractional echo acquisition case and a full echo acquisition case. Thefull echo acquisition can be considered as a special case of thefractional echo acquisition in which Δ=0. The timing relationshipsprovided in Equations (4a)-(4c) are applicable for the FGRE pulsesequence shown in FIG. 6. The FGRE pulse sequence is configured to havea repetition time or period TR and to repeat a total of q times (withdifferent phase-encoding gradient G_(y)(t) for each nth TR, where n=1,2, . . . , q) to acquire a total of q rows of k-space data for a desiredMR image.

After the prepare b(t) step 602, the calculate vibration component steps604-610 are carried out. In the calculate vibration component ofb_(o,n)(t) step 604, phase error φ_(o,n)(t) for the nth TR is calculatedby two terms: (1) the first term covering the time period from the nthα° RF pulse to the beginning of the nth data acquisition window(0≦t≦t₁), and (2) the second term covering the time period during thenth row data acquisition (t₁≦t′≦t) (see FIG. 6). Thus, phase errorφ_(o,n)(t) for the nth TR using the FGRE pulse sequence is given bymodifying Equation (7b) to: $\begin{matrix}{{\varphi_{0,n}(t)} = {{2\quad \pi \quad \gamma {\int_{0}^{t_{1}}{{b_{0,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{b_{0,n}\left( t^{\prime} \right)}{t^{\prime}}}}}}} & (12)\end{matrix}$

where γ is the gyromagnetic constant and b_(o,n)(t) is given in Equation(7a). Notice there is no need to take into account the phase reversaleffect because no refocusing RF pulses are used in the FGRE pulsesequence.

In the calculate vibration component of g_(x,n)(t) step 606, k_(x)-spacedisplacement error Δk_(x,n)(t) for the nth TR using the FGRE pulsesequence is calculated using Equation (12) except substitutingb_(o,n)(t) with g_(x,n)(t) in Equation (8a) to: $\begin{matrix}{{\Delta \quad {k_{x,n}(t)}} = {{2\quad \pi \quad \gamma {\int_{0}^{t_{1}}{{g_{x,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{g_{x,n}\left( t^{\prime} \right)}{{t^{\prime}}.}}}}}} & (13)\end{matrix}$

In the calculate vibration component of g_(y,n)(t) step 608, k_(y)-spacedisplacement error Δk_(y,n)(t) for the nth TR using the FGRE pulsesequence is calculated using Equation (12) except substitutingb_(o,n)(t) with g_(y,n),(t) in Equation (9a) to: $\begin{matrix}{{\Delta \quad {k_{y,n}(t)}} = {{2\quad \pi \quad \gamma {\int_{0}^{t_{1}}{{g_{y,n}(t)}{t}}}} + {2\quad \pi \quad \gamma {\int_{t_{1}}^{t}{{g_{y,n}\left( t^{\prime} \right)}{{t^{\prime}}.}}}}}} & (14)\end{matrix}$

In the calculate vibration component of g_(z)(t) step 610,slice-selection gradient error Δk_(z,n) for the nth TR using the FGREpulse sequence is given by modifying Equation (10) to cover the timeinterval from the nth α° RF pulse to the center of the nth MR echosignal: $\begin{matrix}{{\Delta \quad k_{z,n}} = {2\quad \pi \quad \gamma {\int_{{({n - 1})}{TR}}^{{{({n - 1})}{TR}} + \tau}{{g_{z}(t)}{{t}.}}}}} & (15)\end{matrix}$

Alternatively, Equation (15) may also be expressed as: $\begin{matrix}{{{\Delta \quad k_{z,n}} = {2\quad \pi \quad \gamma {\int_{0}^{\tau}{{g_{z,n}(t)}{t}}}}},} & \text{(15a)}\end{matrix}$

where g_(z,n)(t) is given by Equation (10b).

Using Equations (12)-(15a) to numerically or analytically calculate thevibration error components, the appropriate compensate steps 614-620 canbe carried out to correct the nth row of k-space data as discussedabove. For example, in the compensate step 614, the correction pulse orwaveform would have an area under the pulse of −Δ_(k,n)/2πγ. Moreover,the correction pulse or waveform may be the blip gradient pulse or theadditional crusher or slice refocusing gradient pulse as shown in FIGS.5(a)-5(b), respectively. The correction pulse could be added anywherefrom after the nth α° RF pulse to before the start of the nth echo. Butsince no refocusing RF pulses are utilized, there is no need to negatethe polarity of the correction pulse to offset the phase reversaleffect.

The process would be repeated for the next TR period until all q rows ofk-space data have been corrected of the undesirable presence of magnetvibration. With the corrected k-space data, an MR image is thenreconstructed in reconstruction step 622.

FSE Pulse Function

In still another embodiment of the present invention, the magnetic fieldvibration quantification and compensation scheme is shown applied to anMR image acquired using the FSE pulse sequence. Again, the earlierdescription provided with respect to the SE pulse sequence is applicableto this pulse sequence, with variations in equations and otherparameters discussed below.

Referring to FIG. 7, there is shown a simplified diagram of the FSEpulse sequence. The FSE pulse sequence includes a 90° RF pulse 500, afirst 180° RF pulse 502, a first data acquisition window 504, a second180° RF pulse 506, a second data acquisition window 508, a third 180° RFpulse 510, and a third data acquisition window 512. A reference timepoint of t=0 is set at the center of the 90° RF pulse 500 of a first TR(or shot) of the data acquisition. The first 180° RF pulse 502 followsthe 90° RF pulse 500 after a time interval τ. The first data acquisitionwindow 504 follows the first 180° RF pulse 502 and is turned on at atime t=t₁. After the first data acquisition window 504 is turned off andat an echo spacing (esp) from the first 180° RF pulse 502, the second180° RF pulse 506 is executed. Similarly, the third 180° RF pulse 510 isexecuted after a time interval esp from the second 180° RF pulse 506;and following the second and third 180° RF pulses 506, 510, the secondand third data acquisition windows 508, 512 are executed at times t=t₂and t=t₃, respectively. Each of the windows 504, 508, 512 is turned onfor a time period T.

In this manner, as is well-known in the art, each FSE pulse sequencewill comprise one 90° RF pulse followed by a total of j 180° RF pulses,each 180° RF pulse followed by a corresponding data acquisition window.At each data acquisition window, an echo or a row of raw k-space data isobtained. A total of i such FSE pulse sequences (also referred to as ishots) will be executed to achieve a total of q rows of raw k-spacedata. In other words, for an MR image to be acquired, the FSE pulsesequence needs to be executed i times or shots, each ath shot inducing jechoes and accordingly j rows of k-space data acquisition. The number ofechoes per shot, j, can range from 2 to 128, and preferably j is in therange between 8 to 16. Thus, a total of q=i*j rows of data can beacquired.

Because FSE pulse sequences are more complicated than SE or FGRE pulsesequences, its vibration error components are also more complex.

Among other things, the multiple phase reversal effects caused by the180° RF pulses (i.e., refocusing pulse trains) and stimulated echoescaused by non-ideal refocusing pulse trains need to be taken intoaccount. To simplify calculations, it will be assumed that stimulatedecho pathways can be dephased using non-constant crusher gradientwaveforms, as shown in “High-field MR Microscopy Using Fast SpinEchoes,” by X. Zhou et at., Magnetic Resonance in Medicine, 30:60-67(1993), and are therefore negligible. In actuality, stimulated echopathways are not as easily ignored in FSE pulse sequences; however, suchassumptions permit reasonable approximations when the primary echoesdominate the signals. Under this condition, image artifacts can at leastbe reduced if not eliminated.

For the calculate step 604, b_(o)(t) can be more conveniently expressedwith respect to the ath shot based on similar derivation of Equations(6a)-(7a): $\begin{matrix}{{b_{0,a}(t)} = {\sum\limits_{m = 1}^{M_{0}}{a_{m}\sin \quad \left( {{2\quad \pi \quad f_{m}t} + \zeta_{m,a}} \right)}}} & \text{(16a)}\end{matrix}$

where ζ_(m,a)=2π(a−1)f_(m)Q+ζ_(m,1), Q is the TR time of the FSE pulsesequence, and a=1, 2, . . . , i shots. Now consider b_(0,a)(t) relatingto the first echo (c=1, where c=1, 2, . . . , j echoes) of the ath shot.Analogous to the vibration error component of b_(0,n)(t) for the SEpulse sequence, the vibration component φ_(1,a)(t) of b_(0,a)(t)for thefirst echo of the ath shot is: $\begin{matrix}{{\varphi_{1,a}(t)} = {{- \delta_{1,a}} + {\Delta \quad \varphi_{1,a}} + {2\quad \pi \quad \gamma \quad {\int_{t_{1}}^{t}{{b_{0,a}\left( t^{\prime} \right)}{t^{\prime}}}}}}} & \text{(16b)}\end{matrix}$

whereδ_(1, a) = 2  π  γ∫₀^(τ)b_(0, a)(t)t, Δ  φ_(1, a) = 2  πγ∫_(τ)^(t₁)b_(0, a)(t)t,

 and t₁=esp−T/2. For the second echo (c=2) of the ath shot, thevibration component φ_(2,a)(t) of b_(0,a)(t) is: $\begin{matrix}{{\varphi_{2,a}(t)} = {{- \delta_{2,a}} + {\Delta\varphi}_{2,a} + {2\quad {\pi\gamma}{\int_{t_{2}}^{t}{{b_{0,a}\left( t^{\prime} \right)}{t^{\prime}}}}}}} & (17)\end{matrix}$

whereδ_(2, a) = −δ_(1, a) + 2  πγ∫_(τ)^(3τ)b_(0, a)(t)t, Δφ_(2, a) = 2  πγ∫_(τ)^(t₂)b_(0, a)(t)t,

 and t₂=2esp−T/2.

Thus, a general expression of the vibration component φc,a(t) ofb_(0,a)(t) for any cth echo in the ath shot is given by: $\begin{matrix}{{\varphi_{c,a}(t)} = {{- \delta_{c,a}} + {\Delta \quad \varphi_{c,a}} + {2\quad {\pi\gamma}{\int_{t_{c}}^{t}{{b_{0,a}\left( t^{\prime} \right)}{t^{\prime}}}}}}} & (18)\end{matrix}$

where$\delta_{c,a} = {\sum\limits_{h = 1}^{c}{\theta_{h,a}\left( {- 1} \right)}^{h + {{mod}{({h,2})}}}}$

(the accumulated phase up to the cth 180° RF pulse in the ath shot),$\begin{matrix}{\theta_{1,a} = {2\quad \pi \quad \gamma {\int_{0}^{\tau}{{b_{0,a}(t)}{t}}}}} & {\left( {{{the}\quad {phase}\quad {at}\quad {the}\quad c} = {1\quad 180{^\circ}\quad {RF}\quad {pulse}}} \right)\quad {and}} \\{{\theta_{h,a} = {2\quad {\pi\gamma}{\int_{{({h - 1})}\tau}^{{({h + 1})}r}{{b_{0,a}(t)}{t}}}}},} & \left( {{{for}\quad h} \geq 2} \right)\end{matrix}$

(the phase from (h-1)th to the hth 180° RF pulses),Δ  φ_(c, a) = 2  π  γ∫_((2c − 1)τ)^(t_(c))b_(0, a)(t)t

(the phase from the cth 180° RF pulse to the beginning of the cth dataacquisition window),

t _(c)=2c·τ=T/2

(the starting data acquisition time of the cth echo in the ath shot),and mod(h,2) denotes the remainder of h/2. Hence, each cth echo in theath shot (or in other words, each nth row of k-space data acquired,where n=c+j(a−1)) will have vibration error φ_(c,a)(t) associated withit. Each vibration error φ_(c,a)(t) will be associated with itscorresponding nth k-space row according to the FSE view ordering tables.The FSE view ordering table relates each echo to a nth k-space row suchthat the plurality of echoes emitted in all the shots can be properlyidentified and indexed.

In the calculate step 606, k,-space displacement error Δk_(x,c,a)(t) ofg_(x,a)(t) for the cth echo in the ath shot (in other words the nth rowof k-space data) using the FSE pulse sequence is calculated using anequation similar to Equation (18) but substituting b_(0,a)(t) withg_(x,a)(t). Similarly, in the calculate step 608, k_(y)-spacedisplacement error Δk_(y,c,a)(t) of g_(y,a)(t) for the cth echo in theath shot (in other words the nth row of k-space data) is calculatedusing an equation similar to Equation (18) but substituting b_(0,a)(t)with g_(y,a)(t).

In the calculate step 610, slice-selection gradient error Δk_(z,c,a) ofg_(z)(t) for the cth echo in the ath shot (the nth row of k-space data)is calculated from the ath 90° RF pulse to the center of the cth echo.Slice-selection gradient error Δk_(z,c,a) can be calculated usingEquation (19): $\begin{matrix}{{{\Delta \quad k_{z,c,a}} = {{- \delta_{z,c,a}} + {2\quad {\pi\gamma}{\int_{{({{2c} - 1})}\tau}^{2c\quad \tau}{{g_{z,a}(t)}{t}}}}}},} & (19)\end{matrix}$

where $\begin{matrix}{{\delta_{z,c,a} = {\sum\limits_{h = 1}^{c}{\theta_{z,h,a}\left( {- 1} \right)}^{h + {{mod}{({h,2})}}}}},} & \quad \\{{\theta_{z,1,a} = {2\quad \pi \quad \gamma {\int_{O}^{\tau}{{g_{z,a}(t)}{t}}}}},} & \quad \\{\theta_{z,h,a} = {2\quad \pi \quad \gamma {\int_{{({h - 1})}\tau}^{{({h + 1})}\tau}{{g_{z,a}(t)}{t}}}}} & {\left( {h \geq 2} \right).}\end{matrix}$

As with the phase error φ_(c,a)(t) each of the gradient induced errorsis also correlated to its corresponding nth k-space row according to theFSE view ordering tables.

Once all vibration error components, or k-space phase errors, are known,acquisition of the nth row of k-space data, or more preferably of all jechoes in the ath shot, is initiated in step 612. Next, compensate steps614-620 are carried out to correct the phase errors in the cth echo ofthe ath shot. For example, in compensate step 614, the correction pulseor waveform would have an area under the pulse of −Δk_(z,c,a)/2πγ.

As shown in FIG. 8, the correction pulse, which is added to or combinedwith the slice-selection gradient, can be (a) a blip gradient pulseg_(zcomp,c,a) having an area under the pulse of −Δk_(z,c,a)/(2πγ), or(b) an additional crusher or slice refocusing gradient pulseg′_(zcomp,c,a) also having an area under the pulse of −Δk_(z,c,a)/(2πγ).Preferably, j blip gradient pulses, such as blip gradient pulses710,712,714, etc. having areas under the pulses of −Δk_(z,1,a)/(2πγ),−γk_(z,2,a)/(2πγ), −γk_(z,3,a)/(2πγ), etc., respectively, are applied tothe slide-selection gradient (see FIG. 8(a)). The blip gradient pulsescan be positive or negative pulses. Alternatively, the j compensationgradient pulses can be combined with the existing crusher or slicerefocusing gradient pulses 716,718,720, etc. having additional areas of−Δk_(z,1,a)/(2πγ), −Δk_(z,2,a)/(2πγ), −Δk_(z,3,a)/(2πγ), etc.,respectively (see FIG. 8(b)). Each additional gradient is applied suchthat it occurs after its corresponding refocusing RF pulse. Compensationfor the other errors, φ_(c,a)(t), Δk_(x,c,a)(t) and Δk_(y,c,a)(t), canbe carried out by receiver phase adjustment and k-space regridding asdiscussed for the SE pulse sequence.

The process shown in FIG. 3 will repeat i times to calculate andcompensate for each echo in each shot. After the compensate steps614-620 have been completed, image reconstruction step 222 occurs usingwell-known reconstruction techniques. In this manner, image artifactscaused by undesirable magnet or magnetic field vibrations can beeliminated or reduced in the MR image acquired using the FSE pulsesequence.

While the embodiments of the invention illustrated in the FIGS. anddescribed above are presently preferred, it should be understood thatthese embodiments are offered by way of example only. For example, it iscontemplated that more or less than four vibration components (one b₀field and three linear gradient fields) may be calculated and correctedfor in a given row of k-space data. In another example, image artifactscaused by magnet vibration may also be corrected in three dimensional MRimages. For three dimensional images, the calculate vibration componentof g_(z)(t) step 610 and the compensate step 614 may be replaced withsteps similar to the calculate and compensate vibration component ofg_(y)(t) steps 608, 620. In still another example, each of the vibrationerror components for all q rows of k-space data may be stored in amemory device such that the compensate steps 616-620 need not be carriedout for each nth row of k-space data as it is being acquired. Instead,the compensation may take place after all the rows of k-space data havebeen acquired. It is also contemplated that MR images acquired usingother types of pulse sequences, such as an echo planar imaging (EPI)pulse sequence, may benefit from the present invention. Accordingly, thepresent invention is not limited to a particular embodiment, but extendsto various modifications that nevertheless fall within the scope of theappended claims.

What is claimed is:
 1. A method for quantifying an error associated withacquisition of a magnetic resonance (MR) image, the error produced byvibration of at least one magnet included in an MR imaging system,comprising: identifying a perturbation magnetic field representative ofthe vibration of the at least one magnet, the perturbation magneticfield being present during acquisition of the MR image; and calculatingthe error as a function of the perturbation magnetic field, wherein theerror is at least one of a phase error, a k-space displacement error, ora slice selection gradient error.
 2. The method of claim 1, wherein theperturbation magnetic field includes at least a spatially invariantmagnetic field, a spatially linear readout magnetic field gradient, aspatially linear phase-encoding magnetic field gradient, and a spatiallylinear slice-selection magnetic field gradient.
 3. The method of claim2, wherein calculating the error includes calculating the phase error asa function of the spatially invariant magnetic field.
 4. The method ofclaim 2, wherein calculating the error is repeated for each row of ak-space data set representative of the MR image.
 5. The method of claim2, wherein the k-space displacement error includes a k_(x)-spacedisplacement error and a k_(y)-space displacement error.
 6. The methodof claim 5, wherein calculating the error includes calculating thek_(x)-space displacement error as a function of the spatially linearreadout magnetic field gradient.
 7. The method of claim 5, whereincalculating the error includes calculating the k_(y)-space displacementerror as a function of the spatially linear phase-encoding magneticfield gradient.
 8. The method of claim 2, wherein calculating the errorincludes calculating the slice selection gradient error as a function ofthe spatially linear slice-selection magnetic field gradient.
 9. Themethod of claim 8, wherein the slice selection gradient error iscalculated before acquisition of the MR image.
 10. The method of claim1, wherein calculating the error includes calculating the error as afunction of the perturbation magnetic field and time intervalsassociated with a pulse sequence used to acquire the MR image, the pulsesequence selected from a group including a spin-echo (SE) pulsesequence, a fast gradient echo (FGRE) pulse sequence, and a fast spinecho (FSE) pulse sequence.
 11. An imaging system, comprising: a magnetconfigured to generate a magnetic field to acquire a data setrepresentative of an image of a subject of interest positioned in theimaging system; and a system control in communication with the magnetand configured to calculate an error included in the data set, whereinthe error is associated with vibration of the magnet during acquisitionof the data set and the error is a function of a perturbation magneticfield representative of the vibration of the magnet.
 12. The system ofclaim 11, wherein the perturbation magnetic field includes at least aspatially invariant magnetic field, a spatially linear readout magneticfield gradient, a spatially linear phase-encoding magnetic fieldgradient, and a spatially linear slice-selection magnetic fieldgradient.
 13. The system of claim 12, wherein the error includes a phaseerror and the system control is configured to calculate the phase erroras a function of the spatially invariant magnetic field.
 14. The systemof claim 12, wherein the error includes a slice selection gradient errorand the system control is configured to calculate the slice selectiongradient error as a function of the spatially linear slice-selectionmagnetic field gradient.
 15. The system of claim 12, wherein the errorincludes a k_(x)-space displacement error and the system control isconfigured to calculate the k_(x)-space displacement error as a functionof the spatially linear readout magnetic field gradient.
 16. The systemof claim 12, wherein the error includes a k_(y)-space displacement errorand the system control is configured to calculate the k_(y)-spacedisplacement error as a function of the spatially linear phase-encodingmagnetic field gradient.
 17. The system of claim 11, wherein the errorincludes a slice selection gradient error and the system control isconfigured to calculate the slice selection gradient error beforeacquisition of the data set.
 18. The system of claim 11, wherein thesystem control is configured to calculate the error a plurality oftimes, once for each row of the data set.
 19. The system of claim 11,wherein the system control is configured to calculate the error as afunction of the perturbation magnetic field and time intervalsassociated with the magnetic field.
 20. The system of claim 19, whereinthe magnetic field comprises part of a spin-echo (SE) pulse sequence, afast gradient echo (FGRE) pulse sequence, or a fast spin echo (FSE)pulse sequence.
 21. A system for quantifying an error associated withacquisition of a magnetic resonance (MR) image, the error caused bymagnet vibration present in an MR imaging system, comprising: means foridentifying a perturbing magnetic field representative of the magnetvibration, the perturbing magnetic field being present duringacquisition of the MR image; and means for calculating the error as afunction of the perturbing magnetic field, wherein the error is at leastone of a phase error, a k-space displacement error, or a slice selectiongradient error.
 22. The system of claim 21, wherein the perturbingmagnetic field includes at least a spatially invariant magnetic field, aspatially linear readout magnetic field gradient, a spatially linearphase-encoding magnetic field gradient, and a spatially linearslice-selection magnetic field gradient.
 23. The system of claim 22,wherein the means for calculating is configured to calculate the phaseerror as a function of the spatially invariant magnetic field.
 24. Thesystem of claim 22, wherein the means for calculating is configured tocalculate the error for each row of a k-space data set representative ofthe MR image.
 25. The system of claim 22, wherein the k-spacedisplacement error includes a k_(x)-space displacement error and ak_(y)-space displacement error.
 26. The system of claim 25, wherein themeans for calculating is configured to calculate the k_(x)-spacedisplacement error as a function of the spatially linear readoutmagnetic field gradient.
 27. The system of claim 25, wherein the meansfor calculating is configured to calculate the k_(y)-space displacementerror as a function of the spatially linear phase-encoding magneticfield gradient.
 28. The system of claim 22, wherein the means forcalculating is configured to calculate the slice selection gradienterror as a function of the spatially linear slice-selection magneticfield gradient.
 29. The system of claim 28, wherein the means forcalculating is configured to calculate the slice selection gradienterror before acquisition of the MR image.
 30. The system of claim 21,wherein the means for calculating is configured to calculate the erroras a function of the perturbing magnetic field and time intervalsassociated with a pulse sequence used to acquire the MR image, the pulsesequence selected from a group including a spin-echo (SE) pulsesequence, a fast gradient echo (FGRE) pulse sequence, and a fast spinecho (FSE) pulse sequence.